CN107146211A - Retinal vascular images noise-reduction method based on line spread function and bilateral filtering - Google Patents
Retinal vascular images noise-reduction method based on line spread function and bilateral filtering Download PDFInfo
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Abstract
The invention discloses a kind of retinal vascular images noise-reduction method based on line spread function and bilateral filtering, including：It is that retinal images build the class Gaussian convolution core with different directions and yardstick using line spread function, seek the inner product of the Square Neighborhood and m*n convolution kernel centered on the pixel, obtain direction and the yardstick of convolution kernel corresponding with maximum inner product, utilize the direction of the convolution kernel got, yardstick and line spread function, optimal spatial convolution kernel is calculated for the pixel, it is finally based on the framework of bilateral filtering, the optimal spatial convolution kernel of each pixel is combined with its gray scale convolution kernel, the new filtering convolution kernel of generation, retinal images are filtered using new convolution kernel.Technical scheme ensure that the accuracy of the weight distribution of filtering, improve the effect of vascular protection, and the speed of service of image noise reduction algorithm can be greatly improved.
Description
Technical field
The present invention relates to field of medical image processing, more particularly to a kind of view based on line spread function and bilateral filtering
The method of film blood-vessel image noise reduction.
Background technology
The vessels analysis of retinal images is to diagnose the various ophthalmology diseases of human body and the important evidence of cardiovascular and cerebrovascular disease.Closely
Nian Lai, with the raising of social medical level, retinal vascular images data constantly increase, in order to make up doctor's manual observation and
The efficiency of experience diagnosis is low, the problems such as subjectivity is strong, be increasingly becoming by computer to automatically analyze retinal vascular images
One of necessary means of clinical diagnosis.However, noise in retinal images to retinal vessel automatically analyze bring it is tired
Difficulty, is embodied in the morphosis for destroying blood vessel, reduces the precision of the automatic parsing algorithms such as blood vessel detection and segmentation.Institute
First step during retinal images are automatically analyzed and diagnosed is turned into image noise reduction, is also most basic and crucial one
Step.
Conventional image denoising method can be divided into the method based on gaussian filtering and the method retained based on edge at present.
Method based on gaussian filtering is smoothed using Gaussian function to image, with calculating speed it is fast, be easily achieved etc. it is excellent
Point, still, because gaussian filtering can not retain the marginal texture of image, easily causes image feature information and seriously loses.It is based on
The method that edge retains according to image gray scale in itself or gradient information can protect the edge of image during noise reduction
Feature, is to use most commonly used noise-reduction method at present, however, this method is often only used for handling some simple edge knots
Structure, for contrast in retinal images is relatively low, the unfixed capillary structure of local shape is difficult to be applicable.
Line spread function model, to the theoretical research of optical imagery, is initially used to mould originating from Rossmann in 1969 et al.
Intend a linear light source to spread to both sides in the form of Gaussian cross sectional.Chaudhuri in 1989 et al. has found blood in image
The cross-sectional structure of pipe can be modeled into the line spread function with Gaussian cross sectional, and line spread function model is successfully answered
For detecting blood vessel structure complicated in retinal images, it is proposed that famous matched filtering method is used to detect retinal images
Middle complicated blood vessel structure.
Bilateral filtering is the new image filtering side with reservation edge effect proposed by Tomasi in 1998
Method, is made up of spatial convoluted core and gray scale amplitude convolution kernel two parts, and its Important Thought is to utilize the space length between pixel
The weight of smothing filtering is distributed with the difference of gray value, by parameter regulation to an optimal tradeoff state, is entered to image
The marginal information of image is largely remained while row noise reduction.Side noise-reduction method is protected as most popular image at present,
Bilateral filtering is widely used in multiple fields.But bilateral filtering lacks corresponding function to represent complexity
Blood vessel structure feature, therefore after noise reduction, the relatively low blood vessel of thinner contrast in retinal images can be lost.
Therefore, a technical problem for needing those skilled in the art urgently to solve at present is：How while noise reduction
Artery-sparing structure, improves the degree of accuracy of retinal vessel analysis.
The content of the invention
In order to solve the above problems, present invention incorporates the advantage of line spread function and bilateral filtering, set up a kind of new
Image filtering model, compensate for the bilateral filtering method based on traditional spatial convoluted core and is retaining the relatively low blood capillary of contrast
Deficiency in terms of tubular construction, and using the pretreatment before model realization retinal vascular images segmentation.Expanded using optimal line
Scattered function detects blood vessel structure, local direction and yardstick that can be by the weight of image filtering spatially automatically according to blood vessel
It is allocated；The spatial relationship of pixel can be combined by the framework based on bilateral filtering with gray-scale relation, be further ensured
The accuracy of the weight distribution of filtering, improves the effect of vascular protection.
To achieve these goals, the present invention is adopted the following technical scheme that：
A kind of retinal vascular images noise-reduction method based on line spread function and bilateral filtering, comprises the following steps：
Step 1：A retinal images are chosen, is that the blood vessel in image defines m yardstick and n direction, is expanded using line
It is class Gaussian convolution core of picture construction m*n with different directions and yardstick to dissipate function；
Step 2：For each pixel in retinal images, the Square Neighborhood and m*n centered on the pixel are sought respectively
The inner product of individual convolution kernel, obtains direction and the yardstick of convolution kernel corresponding with maximum inner product；
Step 3：For each pixel in retinal images, the direction of the convolution kernel got, yardstick and line are utilized
Spread function, optimal spatial convolution kernel is calculated for the pixel；
Step 4：Framework based on bilateral filtering, by the optimal spatial convolution kernel of each pixel and its gray scale convolution nuclear phase knot
Close, generate new filtering convolution kernel, retinal images are filtered using new convolution kernel.
Be used to build the line spread function of m*n class Gaussian convolution core in the step 1 be：
And i ∈ (1,2,3...n)；j∈(1,2,3...m)；
Wherein K 'i,j(x, y) is represented in the convolution kernel under i-th of direction and j-th of yardstick, and coordinate is the pixel of (x, y)
Gray value, the convolution kernel mapping in each direction can be gone out by n yardstick by the variances sigma for adjusting Gaussian function, finally given
M*n class Gaussian convolution core；U calculation formula in formula are：
And
Wherein, k represents the length of local square convolution kernel, θiThe blood vessel on i-th of direction and the angle of y-axis are represented,
[x, y] is represented when vessel directions and y-axis angle are 0 °, any point p coordinate in class Gaussian convolution core, and [u, v] represents point p
θ is rotated by convolution kerneliCoordinate behind angle.
Direction is obtained in the step 2 and the formula of yardstick is：
And i, t ∈ (1,2,3...n)；j,s∈(1,2,3...m)
Wherein, p represents some pixel in image, and F (p) is the Square Neighborhood matrix centered on p, K 't,sIt is from m*n
The convolution kernel most matched with vessel directions in F (p) and yardstick that is being selected in individual convolution kernel.
The calculation formula of optimal spatial convolution kernel is in the step 3：
W′s(dvq)=| K 't,s(x, y) |
Wherein, W 'sOptimal spatial convolution kernel is represented, q represents any point in the neighborhood centered on point p；dvqDefinition
The space length of pixel.
The formula of the new filtering convolution kernel of generation is in the step 4：
And
Wherein, I (q) and D (p) represent the input and output value of pixel p respectively, and W () is basic Gaussian function, dvqWith
fpqDefine the space length and Euclidean distance of pixel, kpIt is normalization item；W′s、WrIt is optimal spatial convolution kernel and gray scale volume respectively
Product core, W 'sWrRepresent that the two carries out convolution algorithm.
Further, the optimization content of bilateral filtering framework is included at least one of following：
(1) size and Orientation for getting step 1 is respectively with 1,2,3 ... numeral as n is replaced, and with matrix come
Storage, the language that computer can be recognized is converted into by problem；
(2) optimal spatial convolution kernel is combined with gray scale convolution kernel and generates new filtering core to image filtering in step 4, should
The method that calculating process is filtered using navigational figure is optimized to it；
(3) convolution algorithm is converted into the product calculation in frequency domain by the method changed using frequency domain.
Beneficial effects of the present invention：
1st, on treatment effect, the present invention filters the blood vessel detection based on line spread function with the image based on bilateral filtering
Ripple is combined, while noise reduction is carried out to the image containing blood vessel structure, the blood vessel knot remained in image of high degree
Structure, including the relatively low thin blood vessel structure of contrast.
2nd, in arithmetic speed, first, the line spread function spatial convoluted core in this method is linear, and can be independent
Calculated in gradation of image, therefore calculating speed is very fast；Secondly, can be using " navigational figure ", frequency during filtering
The optimization methods such as domain conversion are optimized to it, further increase arithmetic speed；
3rd, in applicability and autgmentability, because bilateral filtering framework can be applied to most of scene, this method and energy
The blood vessel structure in image is enough protruded, therefore suitable for most of medical image containing blood vessel structure；In addition, bilateral filtering
Gray scale convolution kernel can further expand into gradient, Texture eigenvalue, therefore this method has good autgmentability.
Brief description of the drawings
Fig. 1 is the flow chart of retinal vascular images noise-reduction method of the present invention；
Fig. 2 is the method detection local vascular direction and an example of yardstick using the present invention；
Fig. 3 is traditional spatial convoluted core weight distribution schematic diagram based on Gaussian function；
Fig. 4 is the optimal spatial convolution kernel weight distribution schematic diagram based on line spread function in the present invention；
Fig. 5 is the new convolution kernel generating process schematic diagram in the present invention；
Fig. 6 illustrates an example of the bright processing on the image made by hand of this law；
Fig. 7 illustrates an example of processing of the present invention on real retinal vascular images；
Fig. 8 illustrates an example of the present invention to the pretreatment of some classical blood vessel segmentation algorithm.
Embodiment
Term is explained：
(1) line spread function：Evaluate an important parameter of imaging system images quality, the sunykatuib analysis of line spread function
With verifying that the development to imager is most important.
(2) bilateral filtering:It is a kind of to image protect the wave filter of side noise reduction.
(3) image noise reduction:English name is that Image Denoising. are technical terms in image procossing.In reality
Digital picture is subjected to the influence, referred to as noisy figure such as imaging device and external environmental noise interference in digitlization and transmitting procedure
Picture or noise image.Reduce the process of noise in digital picture and be referred to as image noise reduction, sometimes also known as image denoising.
(4) smothing filtering：The enhanced filter in spatial domain technology of low frequency.Its purpose has two classes：One class is fuzzy；It is another kind of
It is to abate the noise.The smothing filtering of spatial domain is typically carried out using simple average method, exactly seeks the mean flow rate of neighbouring pixel point
Value.The size of neighborhood is directly related with smooth effect, and the more big smooth effect of neighborhood is better, but neighborhood is excessive, can smoothly make
It is bigger that marginal information is lost, so that the image of output thickens, therefore needs the size of reasonable selection neighborhood.
The invention will be further described with embodiment below in conjunction with the accompanying drawings.
Embodiment 1：
Fig. 1 is the flow chart of retinal vascular images noise-reduction method of the present invention.
Need to input before the implementation of whole method and the related parameter that defines is：The retinal vascular images I of noise reduction is treated, is rolled up
Product core long k, and spatial convoluted core and gray difference convolution kernel variances sigmas、σr, and yardstick and the quantity m, n in direction.Through
Many experiments test proves that the optimal parameter for most of retinal vascular images is：K=9；σs=2；σr=0.04；M=
4；N=12.
This method can be summarized as blood vessel detection and image filtering two parts：First with line spread function to retinal map
Blood vessel structure as in is detected, and selects the optimal convolution kernel consistent with image local blood vessel structure, then by the convolution kernel
It is combined with gray scale amplitude convolution kernel, constitutes new image filtering method and noise reduction is carried out to image.
Specifically include following steps：
Step 1：A retinal images are chosen, is that the blood vessel in image defines m yardstick and n direction, is expanded using line
It is class Gaussian convolution core of picture construction m*n with different directions and yardstick to dissipate function formula；
Step 1.1：The total m and n in image mesoscale and direction, input retinal vascular images I are set；
Step 2.2：The class Gaussian convolution core of m different directions is calculated using formula (1) and (2), by adjusting Gaussian function
The convolution kernel mapping in each direction can be gone out n yardstick by several variances sigmas, finally give m*n class Gaussian convolution core.
Wherein K 'i,j(x, y) is represented in the convolution kernel under i-th of direction and j-th of yardstick, and coordinate is the pixel of (x, y)
Gray value.If making k represent the length of local square convolution kernel, θiThe blood vessel on i-th of direction and the angle of y-axis are represented,
Then the u in formula can be calculated by coordinate (x, y) using lower formula：
Wherein, [x, y] represents the class Gauss when vessel directions and y-axis angle are 0 ° (i.e. the direction of blood vessel is parallel with y-axis)
Any point p coordinate in convolution kernel, then [u, v] expression point p is by convolution kernel rotation θiCoordinate behind angle.
Step 2：For each pixel in retinal images, the Square Neighborhood and m*n centered on the pixel are sought respectively
The inner product of individual convolution kernel, compares size and selects maximum inner product, obtains direction and the yardstick of convolution kernel corresponding with maximum inner product, makees
For the local vascular architectural feature of the pixel；
Step 2.1：For each pixel p in image and the Square Neighborhood F (p) centered on p
do
{
1. obtain F (p) and m*n class Gaussian convolution core inner product, i.e. Doti,j=K 'i,j·F(p)；
2. comparing the size for the m*n inner product obtained, the inner product Dot of maximum is therefrom selected, and records inner product correspondence
Filtering core size and Orientation t, yardstick s；
3. record and update the coordinate of pixel.
While (largest index of the pending pixel coordinate value beyond image)；
Wherein, make t, s represent the direction of some pixel local vascular and the yardstick got respectively, then obtain t, s public affairs
Formula is：
Wherein p represents some pixel in image, and F (p) is the Square Neighborhood matrix centered on p, K 't,sIt is from m*n
The filtering core most matched with vessel directions in F (p) and yardstick that is being selected in convolution kernel；
Step 2.2:Export and preserve the neighborhood of pixels of each in image corresponding t and s.
The process of blood vessel structure detection described in step (1) and (2) is as shown in Figure 2.
Step 3：For each pixel in retinal images, spread using the vessel directions got, yardstick and line
Function, an optimal spatial convolution kernel is calculated for the pixel；
Optimal spatial core in the step (3) is the core of the present invention.Make Ws' optimal spatial convolution kernel is represented, q is represented
The value W ' at any point in neighborhood, then q points centered on point ps(dvq) can be by the K ' in formula (3)t,sDraw：
W′s(dvq)=| K 't,s(x, y) | formula (4)
Fig. 3 illustrates the 3 dimensional drawing of Traditional Space convolution kernel weight distribution, and the plane that x, y-axis are determined represents weight point
The position of cloth, z-axis represents the weighted value on relevant position, weighted value WsCalculated by two-dimensional Gaussian function formula：
Wherein dpqRepresent in two dimensional surface, pixel q to point p distance, traditional space it can be seen from the formula
The distance of the weighted value of every bit and the point to central point is in inverse ratio in convolution kernel.
Fig. 4 gives the weight that obtained optimal line spread function spatial convoluted core is calculated in a step 3 of the invention
Convolution kernel in the schematic diagram (3-dimensional stereogram) of distribution, figure is calculated using formula (4), wherein being set with the angle of y-axis
For 0, for handling the blood vessel with y-axis parallel direction.Note the space core and the convolution kernel of traditional Gaussian function in Fig. 2
Difference, the size of its weighted value is in inverse ratio with the distance of pixel to center line.
Step 4：Framework based on bilateral filtering, by the optimal spatial convolution kernel of each pixel and its gray scale convolution nuclear phase knot
Close, generate new filtering convolution kernel, the weighted average of the pixel is calculated using the weight in new convolution kernel.
Optimal spatial convolution kernel is combined with gray scale convolution kernel, generates the weight distribution change during new filtering core
Two and three dimensions schematic diagram.Substantially it is to utilize office using the disposal of gentle filter is carried out in the convolution collecting image for combining generation
The space structure and gray-scale relation of portion's blood vessel are weighted average to pixel.The detailed process of image filtering noise reduction is as follows：
Step 4.1：The total m and n in image mesoscale and direction are set, each variable is initialized：Input retinal vessel figure
As I, Gaussian function variances sigmas、σr, the long k of convolution kernel.
Step 4.2：For each pixel p in image and the Square Neighborhood F (p) centered on p
do
{
1. the result t and s and formula (1), (2), (3) and (4) that are detected using step (2) medium vessels,
The optimal spatial convolution kernel based on line spread function in the neighborhood is calculated, i.e.,：
2. calculating gray scale convolution kernel using the method for traditional bilateral filtering, gray scale convolution kernel formula is：
And fpq=(I (p)-I (q))2
Wherein I (p) and I (q) are 2 points of p, q gray value respectively.
3. formula (4) is utilized by W 'sAnd WrCombine, dot product, and divided by normalization item are asked with F (p).
Wherein, I (q) and D (p) represent the input and output value of pixel p respectively, and W () is basic Gaussian function, dvqWith
fpqDefine the space length and Euclidean distance of pixel, kpIt is normalization item；W′s、WrIt is the optimal sky in the step (4) respectively
Between convolution kernel and gray scale convolution kernel.
4. record and update the coordinate of pixel.
While (largest index of the pixel coordinate value of processing beyond image)；
Optimal spatial core W ' during image filteringsAnd WrThe mode being combined is the convolution algorithm of matrix, can basis
Convolution algorithm theorem：
I(x,y)*w(x,y)<=>F (u, v) H (u, v) formula (7)
Wherein I (x, y), w (x, y) are the weighted value in the value and convolution kernel of image pixel respectively, right respectively in a frequency domain
Answer F (u, v) and H (u, v).Convolution is put into processing in a frequency domain arithmetic speed is significantly improved.
The core ----optimal spatial convolution kernel W of the present invention it can be seen from formula (5)s' value be substantially by filtering
A certain pixel is determined to the distance of the central line of blood vessel in core, and the value in traditional Gaussian spatial convolution kernel is then by picture
The distance of plain point-to-point is determined.Because the part of blood vessel has the complexity such as few number of pixels, tubulose, curvature are smaller, direction is indefinite
Feature, and its local geometric shape can be approximated to be straight line, therefore compared to traditional bilateral filtering, and the present invention can be
Artery-sparing structure while noise reduction, improves the degree of accuracy of retinal vessel analysis.
In order to improve the speed of service of algorithm in implementation process, the present invention enters to traditional bilateral filtering framework base
One-step optimization, the content of optimization mainly includes：
(1) size and Orientation for getting step 1 is respectively with 1,2,3 ... numeral as n is replaced, and with matrix come
Storage, the language that computer can be recognized is converted into by problem.
(2) optimal spatial convolution kernel is combined with gray scale convolution kernel and generates new filtering core to image filtering in step 4, its
Essence is to seek weighted average, and the calculating process can be optimized using the method for famous " navigational figure filtering " to it.
(3) because the basic mode that image filtering is used is convolution algorithm, it is possible to use the method for frequency domain conversion is by convolution
Computing is converted into the product calculation in frequency domain, further improves the speed of service of program.
The present embodiment proposes a kind of retinal vascular images noise-reduction method based on optimal line spread function bilateral filtering.
This method can be summarized as blood vessel detection and image filtering two parts：First with line spread function to the blood in retinal images
Tubular construction is detected, and selects the convolution kernel consistent with image local blood vessel structure, then the convolution kernel and gray scale amplitude are rolled up
Product nuclear phase is combined, and is constituted new image filtering method and is carried out smothing filtering to image.Wherein, visited using optimal line spread function
Blood vessel structure is surveyed, the weight of image filtering can be spatially allocated automatically according to the local direction and yardstick of blood vessel；
The spatial relationship of pixel can be combined by the framework based on bilateral filtering with gray-scale relation, further ensure the weight of filtering
The accuracy of distribution, improves the effect of vascular protection.In addition, the space core based on line spread function computationally need not be all over
Image zooming-out pixel value is gone through, the speed of service of image noise reduction algorithm can be greatly improved in computation amount.
Embodiment 2：
Example of the present invention in the blood-vessel image data made by hand is present embodiments provided, as shown in Figure 6：
Fig. 6 (a) is utilized under Windows7 operating systems, the manual view data that " picture " instrument of utilization is drawn out,
In the picture the pixel value difference of the blood vessel structure of retinal images, blood vessel and background is simulated with darker in color in the straight line of background
For 125 and 180, and a small amount of Gauss or salt-pepper noise are with the addition of with Matlab image processing softwares in the picture.By Fig. 7 (b)
Although as can be seen that traditional bilateral filtering is to picture noise inhibitory action again, but when blood vessel and the contrast of background (c)
When relatively low and thinner, bilateral filtering is highly vulnerable to breakage blood vessel structure.Using the optimal line spread function bilateral filtering energy of the present invention
It is enough to retain while good noise reduction and deepen blood vessel and the contrast of background, preferably enhancing is played to blood vessel structure and is made
With.
Embodiment 3：
Example of the present invention in real retinal vascular images data is present embodiments provided, as shown in Figure 7：
Fig. 7 (a) is a real retinal vascular images, and the image is from famous retinal vessel (database official
Square website：http://www.isi.uu.nl/Research/Databases/DRIVE/) image data base DRIVE the insides are at random
An image selecting and the green channel for taking the image, (b), (c), (d) are to utilize gaussian filtering, bilateral filtering, base respectively
In the noise reduction process result of the bilateral filtering of optimal line spread function.As can be seen that gaussian filtering loses substantial amounts of blood from figure
Tubular construction, by contrast, bilateral filtering can artery-sparing structure, but the relatively low blood vessel structure of thinner in figure contrast also meets with
Destruction is arrived；The method of optimal line spread function bilateral filtering in the present invention is capable of the blood of the reservation different scale of high degree
Pipe, while removing the uneven noise gray scale in image.
Embodiment 4：
Example of the present invention in real retinal vascular images data is present embodiments provided, as shown in Figure 8：
Fig. 8 (a) is Fig. 7 (a) coloured image；Fig. 8 (b) is the green channel of the image；Fig. 8 (c) is the retinal map
As corresponding manual segmentation result, for the standard assessed as image segmentation algorithm；Fig. 8 (d) is straight without noise reduction process
Connect the result detected using famous blood vessel probe algorithm Frangi to blood vessel；Fig. 8 (e) is to utilize traditional bilateral filtering
Noise reduction and then the result detected are carried out to it；Fig. 8 (f) is to carry out noise reduction to image using the method for the present invention, then uses Frangi
The result that method is detected.It is can be found that by contrast：Noise reduction is carried out to image before blood vessel detection, contributes to suppression to scheme
As noise, even but bilateral filtering method popular at present, some thin blood vessels are also destroyed after noise reduction.And it is our
Method compares other two kinds, is capable of the artery-sparing structure of high degree, while reducing the noise of image, improves Subsequent vessel detection
The degree of accuracy.
It will be understood by those skilled in the art that above-mentioned each module of the invention or each step can use general computer
Device realized, alternatively, and the program code that they can be can perform with computing device be realized, it is thus possible to they are deposited
Storage performed in the storage device by computing device, either they are fabricated to respectively each integrated circuit modules or by it
In multiple modules or step single integrated circuit module is fabricated to realize.The present invention is not restricted to any specific hardware
With the combination of software.
Although above-mentioned the embodiment of the present invention is described with reference to accompanying drawing, not to present invention protection model
The limitation enclosed, one of ordinary skill in the art should be understood that on the basis of technical scheme those skilled in the art are not
Need to pay various modifications or deform still within protection scope of the present invention that creative work can make.
Claims (6)
1. a kind of retinal vascular images noise-reduction method based on line spread function and bilateral filtering, it is characterized in that, including it is following
Step：
Step 1：A retinal images are chosen, are that the blood vessel in image defines m yardstick and n direction, letter is spread using line
Number is m*n class Gaussian convolution cores with different directions and yardstick of the picture construction；
Step 2：For each pixel in retinal images, the Square Neighborhood and m*n volume centered on the pixel are sought respectively
The inner product of product core, obtains direction and the yardstick of convolution kernel corresponding with maximum inner product；
Step 3：For each pixel in retinal images, spread using the direction of the convolution kernel got, yardstick and line
Function, optimal spatial convolution kernel is calculated for the pixel；
Step 4：Framework based on bilateral filtering, the optimal spatial convolution kernel of each pixel is combined with its gray scale convolution kernel,
Retinal images are filtered by the new filtering convolution kernel of generation using new convolution kernel.
2. the retinal vascular images noise-reduction method as claimed in claim 1 based on line spread function and bilateral filtering, it is special
Levying is, the line spread function for being used to build m*n class Gaussian convolution core in the step 1 is：
<mrow>
<msubsup>
<mi>K</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
<mo>,</mo>
</msubsup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mo>-</mo>
<msup>
<mi>l</mi>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mfrac>
<msup>
<mi>u</mi>
<mn>2</mn>
</msup>
<mrow>
<mn>2</mn>
<msubsup>
<mi>&sigma;</mi>
<mi>j</mi>
<mn>2</mn>
</msubsup>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
</msup>
</mrow>
And i ∈ (1,2,3...n)；j∈(1,2,3...m)；
Wherein K 'i,j(x, y) is represented in the convolution kernel under i-th of direction and j-th of yardstick, and coordinate is the ash of the pixel of (x, y)
Angle value, n yardstick can be gone out by the variances sigma for adjusting Gaussian function by the convolution kernel mapping in each direction, finally give m*n
Class Gaussian convolution core；U calculation formula in formula are：
<mrow>
<mo>&lsqb;</mo>
<mi>u</mi>
<mo>,</mo>
<mi>v</mi>
<mo>&rsqb;</mo>
<mo>=</mo>
<mo>&lsqb;</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo>&rsqb;</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>cos&theta;</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>sin&theta;</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>sin&theta;</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>cos&theta;</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
And
Wherein, k represents the length of local square convolution kernel, θiRepresent the blood vessel on i-th of direction and the angle of y-axis, [x, y]
The coordinate of any point p in class Gaussian convolution core when vessel directions and y-axis angle are 0 ° is represented, then [u, v] represents that point p passes through
Convolution kernel rotates θiCoordinate behind angle.
3. the retinal vascular images noise-reduction method as claimed in claim 1 based on line spread function and bilateral filtering, it is special
Levying is, direction is obtained in the step 2 and the formula of yardstick is：
<mrow>
<msubsup>
<mi>K</mi>
<mrow>
<mi>t</mi>
<mo>,</mo>
<mi>s</mi>
</mrow>
<mo>,</mo>
</msubsup>
<mo>=</mo>
<munder>
<mrow>
<mi>arg</mi>
<mi>max</mi>
</mrow>
<msubsup>
<mi>K</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
<mo>,</mo>
</msubsup>
</munder>
<mrow>
<mo>(</mo>
<msubsup>
<mi>K</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
<mo>,</mo>
</msubsup>
<mo>&CenterDot;</mo>
<mi>F</mi>
<mo>(</mo>
<mi>p</mi>
<mo>)</mo>
<mo>)</mo>
</mrow>
</mrow>
And i, t ∈ (1,2,3...n)；j,s∈(1,2,3...m)
Wherein, p represents some pixel in image, and F (p) is the Square Neighborhood matrix centered on p, K 't,sIt is from m*n volume
The convolution kernel most matched with the vessel directions and yardstick in F (p) selected in product core.
4. the retinal vascular images noise-reduction method as claimed in claim 3 based on line spread function and bilateral filtering, it is special
Levying is, the calculation formula of optimal spatial convolution kernel is in the step 3：
W′s(dvq)=| K 't,s(x,y)|
Wherein, W 'sOptimal spatial convolution kernel is represented, q represents any point in the neighborhood centered on point p；dvqDefine pixel
Space length.
5. the retinal vascular images noise-reduction method as claimed in claim 4 based on line spread function and bilateral filtering, it is special
Levying is, the formula that new filtering convolution kernel is generated in the step 4 is：
<mrow>
<mi>D</mi>
<mrow>
<mo>(</mo>
<mi>p</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msubsup>
<mi>k</mi>
<mi>p</mi>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msubsup>
<munder>
<mo>&Sigma;</mo>
<mrow>
<mi>q</mi>
<mo>&Element;</mo>
<msub>
<mi>R</mi>
<mi>p</mi>
</msub>
</mrow>
</munder>
<msubsup>
<mi>W</mi>
<mi>s</mi>
<mo>,</mo>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>d</mi>
<mrow>
<mi>v</mi>
<mi>q</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<msub>
<mi>W</mi>
<mi>r</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>f</mi>
<mrow>
<mi>p</mi>
<mi>q</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mi>I</mi>
<mrow>
<mo>(</mo>
<mi>q</mi>
<mo>)</mo>
</mrow>
</mrow>
And
Wherein, I (q) and D (p) represent the input and output value of pixel p respectively, and W () is basic Gaussian function, dvqAnd fpqIt is fixed
The space length and Euclidean distance of adopted pixel, kpIt is normalization item；W′s、WrIt is optimal spatial convolution kernel and gray scale convolution respectively
Core, W 'sWrRepresent that the two carries out convolution algorithm.
6. the retinal vascular images noise-reduction method as claimed in claim 1 based on line spread function and bilateral filtering, it is special
Levying is, wherein, the optimization content of bilateral filtering framework is included at least one of following：
(1) numeral as n that the size and Orientation for getting step 1 is respectively with 1,2,3 ... is deposited to replace with matrix
Storage, the language that computer can be recognized is converted into by problem；
(2) optimal spatial convolution kernel is combined with gray scale convolution kernel and generates new filtering core to image filtering, the calculating in step 4
The method that process is filtered using navigational figure is optimized to it；
(3) convolution algorithm is converted into the product calculation in frequency domain by the method changed using frequency domain.
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